Gsst and applications in optical devices

ABSTRACT

An alloy of GexSbySezTem includes atoms of Ge, Sb, Se, and Te that form a crystalline structure having a plurality of vacancies randomly distributed in the crystalline structure. The alloy can be used to construct an optical device including a first waveguide to guide a light beam and a modulation layer disposed on the first waveguide. The modulation includes the alloy of GexSbySezTem which has a first refractive index n1 in an amorphous state and a second refractive index n2, greater than the first refractive index by at least 1, in a crystalline state. The first waveguide and the modulation layer are configured to guide about 1% to about 50% of the light beam in the modulation layer when the alloy is in the amorphous state and guide no optical mode when the alloy is in the crystalline state.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the priority benefit under 35 U.S.C. § 119(e) ofU.S. Application No. 62/478,717, filed Mar. 30, 2017, and entitled“GE—SB—SE—TE MATERIALS AND OPTICAL DEVICES INCORPORATING SAME,” which ishereby incorporated herein by reference in its entirety.

GOVERNMENT SUPPORT

This invention was made with Government support under Grant No.FA8702-15-D-0001 awarded by the U.S. Air Force. The Government hascertain rights in the invention.

BACKGROUND

Phase change materials (PCMs), such as GeSbTe (GST), are able to beswitched between amorphous and crystalline states upon the applicationof an electrical pulse or a laser pulse. Their material properties, suchas conductivity, bandgap, and refractive index, are distinct in the twostates. Due to this property, PCMs have been widely used to constructelectronic non-volatile memories.

PCMs may also be used for constructing optical devices, which have awide range of applications, such as sensing, imaging, and cognitiveoptical networks. For example, optical switching, i.e., dynamic routingof light into different paths, is widely used in photonic integratedcircuits. Current on-chip optical switches are mostly based onelectro-optical or thereto-optical effects, which usually produce smallrefractive index perturbations (e.g., typically well below 0.01).Therefore, the resulting devices often have a large footprint andsignificant energy consumption. In addition, switching mechanisms basedon electro-optic or thereto-optical effects are volatile, so acontinuous power supply is often used to maintain the optical switchingstate, thereby further increasing the energy consumption.

In recent years, optical devices based on PCMs have emerged for on-chipswitching and routing. PCMs can generate a large difference in therefractive index during phase transition. In addition, a phasetransition in a PCM can be nonvolatile, thereby allowing self-holding orlatching in the resulting optical switches in the absence of power.

Despite these attractive features, the performance of existing PCM-basedphotonic switches is typically compromised by the high opticalabsorption in traditional PCMs. The two most commonly used PCMs includeVO₂ and Ge₂Sb₂Te₅ (i.e., GST 225), both of which suffer from excessiveoptical losses even in their dielectric states. For example, theextinction coefficient (i.e., imaginary part of the refractive index) ofamorphous GST is about 0.12 at 1550 nm wavelength, corresponding toabout 42,000 dB/cm attenuation, which is unacceptably high for manyguided-wave device applications.

SUMMARY

Embodiments of the present technology generally relate to GSST materialsand their applications in optical devices. In one example, an alloy ofGe_(x)Sb_(y)Se_(z)Te_(m) is disclosed and atoms of Ge, Sb, Se, and Te inthe alloy form a crystalline structure having a plurality of vacanciesrandomly distributed in the crystalline structure.

In another example, a method of modulating a light beam propagating in awaveguide includes heating a modulation layer, in optical communicationwith the waveguide, to a first temperature. The modulation layerincludes an alloy of Ge_(x)Sb_(y)Se_(z)Te_(m) switchable between anamorphous state and a crystalline state. The first temperature isgreater than a phase transition temperature of the alloy and less thanabout 100 degrees Celsius above the phase transition temperature. Theheating causes the alloy to form a crystalline structure having aplurality of vacancies randomly distributed in the crystallinestructure.

In yet another example, an apparatus includes a first waveguide to guidea light beam and a modulation layer disposed on the first waveguide. Themodulation includes an alloy of Ge_(x)Sb_(y)Se_(z)Te_(m) having a firstrefractive index n₁ in an amorphous state and a second refractive indexn₂, greater than the first refractive index by at least 1, in acrystalline state. The first waveguide and the modulation layer areconfigured to guide about 1% to about 50% of the light beam in themodulation layer when the alloy is in the amorphous state.

It should be appreciated that all combinations of the foregoing conceptsand additional concepts discussed in greater detail below (provided suchconcepts are not mutually inconsistent) are contemplated as being partof the inventive subject matter disclosed herein. In particular, allcombinations of claimed subject matter appearing at the end of thisdisclosure are contemplated as being part of the inventive subjectmatter disclosed herein. It should also be appreciated that terminologyexplicitly employed herein that also may appear in any disclosureincorporated by reference should be accorded a meaning most consistentwith the particular concepts disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are forillustrative purposes and are not intended to limit the scope of theinventive subject matter described herein. The drawings are notnecessarily to scale; in some instances, various aspects of theinventive subject matter disclosed herein may be shown exaggerated orenlarged in the drawings to facilitate an understanding of differentfeatures. In the drawings, like reference characters generally refer tolike features (e.g., functionally similar and/or structurally similarelements).

FIGS. 1A-1C illustrate the atomic structure of an alloy ofGe_(x)Sb_(y)Se_(z)Te_(m) in different states.

FIG. 2 is measured resistivity of a Ge₂Sb₂Se₄Te₁ alloy as a function oftemperature.

FIGS. 3A and 3B are measured refractive indices and extinctioncoefficients of Ge₂Sb₂Te₅ and Ge₂Sb₂Se₄Te₁ in the amorphous state andcrystalline state, respectively.

FIG. 4 shows x-ray diffraction (MRD) measurements of a Ge₂Sb₂Se₄Te₁alloy after annealing at different temperatures.

FIGS. 5A and 5B show measured refractive indices and extinctioncoefficients, respectively, of a Ge₂Sb₂Se₄Te₁ alloy after annealing atdifferent temperatures.

FIG. 6 shows a schematic of an optical device including an alloy ofGe_(x)Sb_(y)Se_(z)Te_(m) for light beam modulation.

FIGS. 7A-7B show simulated intensity profiles of even supermodes and oddsupermodes in a two-waveguide system when the GSST is in the amorphousstate.

FIGS. 7C-7D show simulated intensity profiles of even supermodes and oddsupermodes, respectively, in the two-waveguide system shown in FIGS.7A-7B when the GSST is in the crystalline state.

FIGS. 8A and 8B show a cross sectional view and a perspective view of anoptical switch using GSST alloy for light routing.

FIGS. 8C and 8D show simulated optical field of the switch shown inFIGS. 8A and 8B when the GSST in the modulation layer is in theamorphous state and the crystalline state, respectively.

FIGS. 8E and 8F are calculated insertion loss and crosstalk,respectively, of the switch shown in FIGS. 8A and 8B across the telecomC-band.

FIGS. 9A and 9B show a cross sectional view and a perspective view,respectively, of a 2×2 optical switch using GSST alloy for lightrouting.

FIGS. 9C and 9D show a simulated optical field of the 2×2 switch shownin FIGS. 9A and 9B when the GSST in the modulation layer is in theamorphous state and the crystalline state, respectively.

FIGS. 9E and 9F are calculated insertion loss and crosstalk,respectively, of the 2×2 switch shown in FIGS. 9A and 9B across thetelecom C-band.

FIG. 10A shows a schematic of an 8×8 Benes network based on nonvolatileswitches using GSST alloy.

FIG. 10B shows a schematic of a 2^(m)×2^(m) Benes network 1000illustrating the recurrence relation between a 2^(m)×2^(m) switch and2^(m−1)×2^(m−1) switch.

FIG. 10C shows the all-bar and all-cross insertion losses versus thenetwork level in in the 2^(m)×2^(m) Benes network shown in FIG. 10B.

FIG. 11A shows a schematic of a modulator including a ring resonator anda modulation layer made of a GSST alloy.

FIG. 11B is a microscope image of two modulators similar to themodulator in FIG. 11A.

FIG. 11C shows transmission spectra of the modulator shown in FIG. 11Awhen the GSST is in the crystalline state and the amorphous state.

FIG. 12 shows a schematic of an interferometer using GSST alloy forphase modulation.

FIG. 13 shows a schematic of a pixel array integrated with a GSST alloyfor light modulation.

FIGS. 14A-14D illustrate a method of manufacturing GSST alloys.

FIG. 15 shows a schematic of a system to fabricate GSST films viathermal deposition.

FIG. 16 shows a schematic of a system to fabricate GSST film viasputtering.

DETAILED DESCRIPTION

CSST Alloy

To address the challenges in conventional optical devices using phasechange materials (PCMs), a new alloy of Ge_(x)Sb_(y)Se_(z)Te_(m) isengineered to have low optical loss in the optical and near infraredregime and a large difference in the refractive index greater than 1)for different phases or states. The alloy of Ge_(x)Sb_(y)Se_(z)Te_(m)includes four elements, germanium (Ge), antimony (Sb), selenium (Se),and tellurium (Te), and vacancies distributed among these atoms. The lowoptical loss can be attributed to the atomic structure of the alloy inits crystalline state, in which atoms of Ge, Sb, Se, and Te form acrystalline structure (i.e., ordered structure) while multiple vacanciesare randomly distributed in the crystalline structure. To realize thisatomic structure, an annealing step can be performed on the alloy in theamorphous state. The annealing temperature is within the window betweenthe phase transition temperature of the alloy and about 100° C. abovethe phase transition temperature. Within this window, the annealing cancause the atoms of Ge, Sb, Se, and Te to form a crystalline structurewithout creating ordered distribution of vacancies. Without being boundby any particular theory or mode of operation, a disordered distributionof vacancies can introduce the Anderson-localization effect, which canlocalize the carriers and decrease the carrier mobility, therebyproviding low free carrier loss.

FIGS. 1A-1C show atomic structures of the alloy Ge_(x)Sb_(y)Se_(z)Te_(m)in different states (also referred to as different phases). FIG. 1Ashows an atomic structure 101 when the alloy Ge_(x)Sb_(y)Se_(z)Te_(m) isin a crystalline state after proper annealing (more details of theannealing process are provided below). In this atomic structure 101, theatoms of Ge (110), Sb (120), Se (130), and Fe (140) form a crystallinestructure, i.e., these atoms 110 to 140 are arranged in an orderedconfiguration. The atomic structure 101 also includes multiple vacancies150 randomly distributed within the crystalline structure formed by theatoms 110 to 140. The atomic density of the vacancies 150 in the alloycan be, for example, from about 0.5 at. % to about 20 at. % (e.g., about0,5 at. %, about 1 at. %, about 2 at. %, about 3 at. %, about 4 at. %,about 5 at. %, about 6 at. %, about 7 at. %, about 8 at. %, about 9 at.%, about 10 at. %, about 12 at. %, about 14 at. %, about 16 at. %, about18 at. %, or about 20 at. %, including any values and sub ranges inbetween).

FIG. 1B shows an atomic structure 102 for the Ge_(x)Sb_(y)Se_(z)Te_(m)alloy in the amorphous state. In this atomic structure 102, the atoms110 to 140 are randomly distributed. The atomic structures 101 and 102shown in FIG. 1A and 1B, respectively, can be used to construct opticaldevices. The transition from the amorphous state to the crystallinestate can be realized by increasing the temperature of theGe_(x)Sb_(y)Se_(z)Te_(m) alloy (e.g., between phase transitiontemperature and 100° C. above the phase transition temperature). Thereverse transition (i.e., from the crystalline state to the amorphousstate) can be realized by further increasing the temperature of thealloy, followed by a fast cooling process. More details below about theapplication of the alloy Ge_(x)Sb_(y)Se_(z)Te_(m) in optical devices areprovided below with reference to FIGS. 6-13.

For comparison, FIG. 1C shows an atomic structure 103 of theGe_(x)Sb_(y)Se_(z)Te_(m) alloy formed by over annealing (e.g., annealingat a temperature higher than a threshold temperature). In the atomicstructure 103, the atoms 110-140 form a crystalline structure and thevacancies 150 are also aligned along a straight line to form an orderedarrangement. Compared to the atomic structure 101 shown in FIG. 1A, theatomic structure 103 in FIG. 1C usually has a higher optical loss.

The alloy Ge_(x)Sb_(y)Se_(z)Te_(m) described herein can include variouscompositions (e.g., different atomic percentages of each element).Selenium has a smaller atomic number than tellurium and is a good glassformer. In generally, substituting Te with Se (e.g., in conventionalGST) can increase the bandgap as well as decrease the optical loss ofthe resulting alloy.

In one example, x+y is about 0.4 to about 0.5 (e.g., about 0.4, about0.42, about 0.44, about 0.46, about 0.48, or about 0.5, including anyvalues and sub ranges in between), z is from about 0.1 to about 0.54(e.g., about 0.1, about 0.2 about 0.3, about 0.4, about 0.5, about 0.52,or about 0.54, including any values and sub ranges in between), andx+y+z+m=1.

In another example, x can be less than 0.15 (e.g., about 0.15, about0.14, about 0.13, about 0.12, about 0.11, about 0.1, about 0.08, about0.06, about 0.04, or lower, including any values and sub ranges inbetween), y is about 0.5 to about 0.68 (e.g., about 0.5, about 0.52,about 0.54, about 0.56, about 0.58, about 0.6, about 0.62., about 0.64,about 0.66, or about 0.68, including any values and sub ranges inbetween), z is from about 0.05 to about 0.3 (e.g., about 0.05, about0.1, about 0.15, about 0.2, about 0.25, or about 0.3, including anyvalues and sub ranges in between), and x+y+z+m=1.

The compositions of the Ge_(x)Sb_(y)Se_(z)Te_(m) alloy can also beexpressed in terms of atomic percentages. In general, a higher atomicpercentage of Se can decrease the optical loss of the resulting alloybut may also slow down the crystallization process during phasetransition. In practice, at least the following compositions can beused. In one example, the Ge_(x)Sb_(y)Se_(z)Te_(m) alloy can includeabout 0 to 50 at. % of Ge, about 0 to about 50 at. % of Sb, about 5 at.% to about at. 50% of Te, about 10 at. % to about 55% of Se, and the sumof atomic percentages of all elements in the alloy is 100 at. %.

In another example, the Ge_(x)Sb_(y)Se_(z)Te_(m) alloy can include about0 at. % to about 15 at. % of Ge, about 50 at. % to about 70 at. % of Sb,about 2 at. % to about 30 at., of Te, about 5 at. % to about 30 at. % ofSe, and the sum of atomic percentages of all elements in the alloy is100 at. %.

In yet another example, the Ge_(x)Sb_(y)Se_(z)Te_(m) alloy can includeabout 0 at. % to about 45 at. % of Ge, about 0 at. % to about 50 at. %of Sb, about 5 at. % to about 45 at. % of Te, about 10 at. % to about 55at. % of Se, and the sum of atomic percentages of all elements in thealloy is 100 at. %.

In yet another example, the Ge_(x)Sb_(y)Se_(z)Te_(m) alloy can includeabout 0 at. % to about 10 at. % of Ge, about 50 at. % to about 70 at. %of Sb, about 2 at. % to about 30 at. % of Te, and about 5 at. % to about30 at. % of Se, and the sum of atomic percentages of all elements in thealloy is 100 at. %.

The Ge_(x)Sb_(y)Se_(z)Te_(m) alloy described herein can be characterizedby various properties. For example, the phase change temperature To(also referred to as the transition temperature) of the alloy can beabout 150° C. to about 400° C. (e.g., about 150° C., about 200° C.,about 250° C., about 300° C., about 350° C., or about 400 DC, includingany values and sub ranges in between) The phase change temperature T_(c)can also determine the annealing temperature that is used to transitionthe alloy from the amorphous state to the crystalline state. Forexample, the annealing temperature can be about T_(c) to aboutT_(c)+100° C. (e.g., about T_(c), about T_(c)+20° C., about T_(c)+40°C., about T_(c)+60° C., about T_(c)+80° C., or about T_(c)±100° C.,including any values and sub ranges in between).

The resistivity of the Ge_(x)Sb_(y)Se_(z)Te_(m) alloy (in amorphousstate and crystalline state) can be substantially equal to or greaterthan about 1 Ω·cm (e.g., about 1 0.cm, about 2 Ω·cm, about 3 Ω·cm, about5 Ω·cm, about 10 Ω·cm, or greater, including any values and sub rangesin between). Correspondingly, the conductivity of theGe_(x)Sb_(y)Se_(z)Te_(m) alloy can be substantially equal to or lessthan about 1 S/cm (e.g., about 1 S/cm, about 0.5 S/cm, about 0.3 S/cm,about 0.2 S/cm, about 0.1 S/cm, or less, including any values and subranges in between). Higher resistivity corresponds to lower conductivityand can lead to lower free carrier absorption. Therefore, optical lossesof the alloy is also lower.

The complex refractive index N of the Ge,ShySe_(z)Te_(m) alloy can begenerally written as N=n+ik where n is the real part of the refractiveindex and k is the imaginary part of the refractive index (also referredto as the extinction coefficient throughout this Application). The alloyhas distinct refractive indices N₁ and N₂ in the amorphous state and thecrystalline state, respectively. More specifically, N₁=n₁+ik₁, andN₂=n₂+ik₂.

In optical devices, such as optical switches and modulators, it can behelpful to have a large difference between n₁ and n₂, also referred toas the refractive index difference Δn, so as to achieve more efficientmodulation of light beams. The alloy Ge_(x)Sb_(y)Se_(z)Te_(m) describedherein can provide a refractive index difference Δn greater than 1(e.g., about 1, about 1.1, about 1,2, about 1.3, about 1.4, about 1.5,about 1.6, about 1.7, about 1.8, or greater, including any values andsub ranges in between) when it switches between phases.

The extinction coefficient k in the complex refractive index N usuallydetermines the optical losses of Ge_(x)Sb_(y)Se_(z)Te_(m).Ge_(x)Sb_(y)Se_(z)Te_(m), in the crystalline state, can have anextinction coefficient k₂ substantially equal to or less than 10⁻³(e.g., about 10⁻³, about 5×10⁻⁴, about 10⁻⁴, about 5×10⁻⁵, or less,including any values and sub ranges in between). The extinctioncoefficient k₁ of the alloy in the amorphous state is usually evensmaller than k₂. For example, the, k₁ can be negligible in the mid-IRwavelengths and around 10⁻⁴ or less in telecomm wavelength (e.g. about1260 nm to about 162 nm),

The impact of loss on the performance of optical devices is usuallyquantified using the material figure-of-merit FOM=Δn/k, where k is theextinction coefficient of the PCM in the crystalline state. This FOM isquantitatively correlated with the insertion loss (IL) and contrastratio in all-optical, electro-optical, and magneto-optical devices.Conventional PCMs, such as VO₂ and GST, usually have low FOMs of about0.7 and 2.1, respectively, at 1550 nm. As a result, switches based onthese materials have high ILs (e.g., about 2 dB or more) and limitedcrosstalk (e.g., less than about 15 dB in the C-band). As used herein,the crosstalk refers to the contrast ratio between the on/off states atthe output ports (e.g., of an optical switch). In contrast, the alloyGe_(x)Sb_(y)Se_(z)Te_(m) described herein can provide a high FOM due tothe large refractive index change and the small extinction coefficient.For example, the FOM of the alloy Ge_(x)Sb_(y)Se_(z)Te_(m) can besubstantially equal to or greater than 4 (e.g., about 4, about 5, about10, about 20, about 30, about 50, about 100, about 200, about 300, about500, about 1000, or greater, including any values and sub ranges inbetween).

Experimental Characterizations of GSST Alloy

FIG. 2 shows measured resistivity of a Ge₂Sb₂Se₄Te₁ alloy as a functionof temperature. As the temperature increases, the alloy enters the phasetransition region where the resistivity of the alloy decrease sharply.After phase transition, the resistivity continues to decrease due to theordering of vacancies. When the alloy is annealed to T1 or T2, the alloycan still maintain insulating charge transport behavior. When theannealing temperature increases even further, for example, to T3, thealloy starts to become metallic. In optical applications, infraredabsorption is mainly induced by free carrier loss. Therefore, theoptical loss increases as the alloy becomes metallic.

FIGS. 3A and 3B are measured refractive indices and extinctioncoefficients of Ge₂Sb₂Te₅ and Ge₂Sb₂Se₄Te₁ in the amorphous state andcrystalline state, respectively. The measurements were performed usingellipsometry on thermally evaporated films of the alloys. The refractiveindex difference of the GSST sample is greater than 1 within a largespectral window (e.g., above 800 nm). It can also be seen from FIGS. 3Aand 3B that GSST exhibits lower optical loss in both amorphous andcrystalline states compared to GST. The FOM of GSST is about 4.2 at 1550nm, about twice that of the GST sample. In addition, optical attenuationin amorphous GSST, as indicated by the extinction coefficient shown inFIG. 3A, is vanishingly small in the telecom window and well below thesensitivity limit of the ellipsometry. A waveguide cut-back method wastherefore employed to quantify the loss in the amorphous GSST and themeasured extinction coefficient k is about 1.8±1.2×10⁻⁴, which is over600 times smaller than that of GST.

FIG. 4 shows x-ray diffraction (XRD) measurements of a Ge₂Sb₂Se₄Te₁alloy after annealing at different temperatures, from about 150° C. toabout 300° C., for about 30 minutes. The alloy is derived by replacing80% of the Te in Ge₂Sb₂Te₅ with Se. The sharp peaks in the top curve(i.e., annealed at 300° C.) indicate that the alloy is in thecrystalline state.

FIGS. 5A and 5B show measured refractive indices and extinctioncoefficients, respectively, of a Ge₂Sb₂Se₄Te₁ alloy after annealing atdifferent temperatures (in the crystalline state). The refractive indexand the extinction coefficient of the alloy in the amorphous state isalso shown. FIG. 5A shows that the refractive index change after phasetransition is at a level greater than 1 over a wide spectral range(e.g., greater than 1000 nm or 1 μm). The extinction coefficientmeasurements in FIG. 5B demonstrate that reducing the annealingtemperature from about 350° C. to about 250° C. (close to the phasetransition temperature) can significantly lower the optical losses. Inaddition, the conductivity of the alloy after annealing at 350° C. and250° C. is about 18 S/cm and 0.39 S/cm, respectively. The FOMs of thealloy after annealing at 350° C. and 250° C. are about 46 and 9.1,respectively. These FOMs are already significantly higher than thoseachieved in conventional PCMs, such as GST.

Optical Devices Including GSST

The phase change materials described herein can be used in various typesof optical devices, such as optical switches and modulators, due totheir low losses in the optical regime. As shown in thecharacterizations above (e.g., FIGS. 3A and 3B), the FOM of GSST ispredominantly limited by the moderate loss in its crystalline state. Forexample, at 1550 nm, c-GSST's extinction coefficient is about 0.42,which is much lower than that of c-GST but is still high for guided-wavedevices.

Close inspection of the FOM reveals that its derivation builds on anunderlying assumption: the material property modulation during theswitching operation (i.e., phase transition) is sufficiently small suchthat perturbations to the optical mode comprise a high-order effect andare usually neglected. Under this condition, the modal overlap with thePCM can be characterized by a single parameter, i.e., the confinementfactor Γ. Both the desired phase shift (induced by Δn) and the unwantedoptical loss (imposed by k) scale with Γ. The small perturbationassumption applies to devices relying on traditional electro-optic,thermo-optic, all-optical, and magneto-optical mechanisms. Therefore,the performance of these devices is usually bound by the FOM, regardlessof the specific device configuration (e.g., Mach-Zehnder interferometers(MZIs), directional couplers (DCs), or micro-ring resonators).

The large optical property contrast between the two states in the alloyof GSST, however, permits different modal confinement factors in the twostates. For example, the device can be engineered to have large modalconfinement within the GSST layer when the GSST is in the low-lossamorphous state, and minimal optical field overlap with GSST when theGSST is switched to the crystalline state. This configuration isreferred to as a “non-perturbative” design and can achieve low-loss,high-contrast modulation (e.g., switching) beyond the classicalperformance limits set forth by the material FOM.

FIG. 6 shows a schematic of an optical device 600 including an alloy ofGe_(x)Sb_(y)Se_(z)Te_(m) for light beam modulation. The device 600includes a waveguide 610 to guide a light beam and a modulation layer620 disposed on the waveguide 610 to modulate the light propagating inthe waveguide 610. The device 600 can also include an optional cladding630 surrounding the waveguide 610. The cladding 630 can have arefractive index smaller than the refractive index of the waveguide 610.For example, the waveguide 610 can include silicon nitride (SiN) and thecladding 630 can include silicon oxide. In another example, the cladding630 can be ambient air.

The modulation layer 620 includes the GSST alloy described herein. Acontroller 640 can be used to switch the GSST alloy between theamorphous state and the crystalline state. In one example, thecontroller 640 includes a heat source to increase the temperature of themodulation layer to the annealing temperature (e.g., above the phasetransition temperature but less than 100° C. above the phase transitiontemperature) so as to switch the GSST alloy into the crystalline state.In another example, the controller 640 can include a laser to heat themodulation layer 620 using optical pulses or beams. In the crystallinestate, the modulation layer 620 may have some optical losses and thewaveguide 610 can be configured to guide almost all the light beam(i.e., negligible propagation in the modulation layer 620).

The controller 640 is also able to further increase the temperature ofthe GSST alloy to be higher than the melting temperature of the alloy(e.g., about 600° C. or higher), followed by a fast cooling process, toswitch the GSST alloy back to the amorphous state. The cooling rate canbe, for example, about 10⁵° C. per second or greater (e.g., about 10⁵°C. per second, about 5×10⁵° C. per second, about 10⁶° C. per second, orgreater, including any values and sub ranges in between). This highcooling rate can be achieved by, for example, reducing the thickness ofthe modulation layer 620. For example, the thickness of the modulationlayer 620 can be about 1 mm or less (e.g., about 1 mm, about 500 μm,about 200 μm, about 100 μm, about 50 μm, about 20 μm, about 10 μm, about5 μm, about 2 μm, about 1 μm, about 500 nm, about 200 nm, about 100 nm,or less, including any values and sub ranges in between).

Since GSST in the amorphous state has very low optical loss, part of thelight beam can be guided in the modulation layer. For example, themodulation layer 620 can be configured to guide about 1% to about 50% ofthe optical power in the light beam (e.g., about 1%, about 2%, about 5%,about 10%, about 20%, about 30%, about 40%, or about 50%, including anyvalues and sub ranges in between). To facilitate the change of modepropagation induced by the phase transition of the GSST alloy, therefractive index of the waveguide 610 can be substantially identical tothe refractive index of the modulation layer 620 in the amorphous state.When the GSST alloy transitions to the crystalline state, its refractiveindex can change by more than 1 and thus become very different from therefractive index of the waveguide 610. Accordingly, optical modes can bepushed out of the modulation layer 620 and confined within the waveguide610.

In operation, a method of modulating a light beam propagating in thewaveguide 610 includes heating the modulation layer 620 to a firsttemperature, which is greater than the phase transition temperature ofthe alloy and less than about 100 degrees Celsius above the phasetransition temperature (i.e., between T_(c) and T_(c)+100° C., whereT_(c) is the phase transition temperature). For example, the firsttemperature used in the annealing process can be about 200° C. to about350° C. (e.g., about 200° C., about 250° C., about 300° C., or about350° C., including any values and sub ranges in between). The heatingprocess is also referred to as an annealing process and causes the alloyto form a crystalline structure having a plurality of vacancies randomlydistributed in the crystalline structure. In one example, a heater canbe used to increase the temperature of the modulation layer 620. Inanother example, a laser pulse can be used to increase the temperatureof the modulation layer 620.

The device 600 shown in FIG. 6 can be extended to a general structureincluding a first optical element and a second optical element disposedin optical communication with the first optical element. The secondoptical element is made of the GSST alloy described herein. The firstoptical element is configured to provide optical confinement of a lightbeam and the second optical element is configured to modulateelectromagnetic field distribution within the first optical element. Inone example, the second optical element can be disposed on the firstoptical element. In another example, the second optical element can bedisposed within the first optical element. In yet another example, thesecond optical element can be separated from the first optical elementby a third element.

The device 600 shown in FIG. 6 is a building block that can be used toconstruct various other optical devices. FIGS. 7A-7B show simulatedintensity profiles of even supermodes and odd supermodes in atwo-waveguide system when the GSST is in the amorphous state. FIGS.7C-7D show simulated intensity profiles of even supermodes and oddsupermodes, respectively, in the two-waveguide system when the GSST isin the crystalline state. The two-waveguide system includes twowaveguides disposed in parallel with each other. A modulation layer madeof GSST is disposed on the right waveguide and not on the leftwaveguide. In these simulations, the two waveguides are made of SiN andhave the same core height. In addition, the widths of the two waveguidesare adjusted such that their effective indices are identical when theGSST is amorphous. As a result, the phase matching can lead to strongcoupling between the two waveguides with well-defined even (symmetric)and odd (antisymmetric) supermodes (see FIGS. 7A and 7B). In contrast,the large effective index disparity between the two waveguides when theGSST is in the crystalline state results in two isolated modes (seeFIGS. 7C and 7D).

In operation, the system can be configured to allow only the odd modes(shown in FIGS. 7B and 7D) to be excited, thereby allowing guiding oflight in the modulation layer with amorphous GSST (FIG. 7B) andprohibiting guiding of light in the modulation layer with crystallineGSST (FIG. 7D). For example, light can be delivered into bare waveguide(i.e. left waveguide without the GSST layer). When the GSST isamorphous, the strong coupling in FIGS. 7A and 7B can route the lightfrom the left waveguide to the right waveguide capped with the GSST.When GSST is crystalline, the indices in FIGS. 7C and 7D are sodifferent that the strong coupling disappears. Therefore the lightremains in the left waveguide. Since negligible amount of light iscoupled to the GSST capped waveguide, the crystalline GSST does notinduce loss in the optical propagation.

FIGS. 8A and 8B show a cross sectional view and a perspective view,respectively, of an optical switch 800 using GSST alloy for lightrouting. The optical switch 800 includes a first waveguide 810 a and asecond waveguide 810 b. At least a portion of the second waveguide 810 bis parallel to the first waveguide 810 a. A modulation layer 820 made ofthe GSST alloy described herein is disposed on the first waveguide 810a. The optical switch 800 can also include an optional cladding 830(e.g., silicon oxide) surrounding the two waveguides 810 a and 810 b.

As illustrated in FIG. 8A, the width we of the first waveguide 810 a issubstantially identical to the spacing w_(g) between the two waveguides810 a and 810 b, i.e., w_(c)=w_(g) (e.g., about 500 nm). The width w_(s)(e.g., about 720 nm) of the second waveguide 810 b is slightly greaterthan the width w_(c), of the first waveguide 810 a to ensure that theeffective index of the second waveguide 810 b is the same as theeffective index of the combination of the first waveguide 810 a and themodulation layer 820 (in amorphous state). The width w_(p) (e.g., about400 nm) of the modulation layer 820 can be less than the width we of thefirst waveguide 810 a. The heights h of the two waveguides 810 a and 810b are identical (e.g., about 450 nm) and the height h_(p) of themodulation layer 820 can be less than the height h (e.g., about 60 nm),

FIGS. 8C and 8D show simulated optical field in the switch 800 when theGSST in the modulation layer 820 is in the amorphous state and thecrystalline state, respectively. FIGS. 8E and 8F are calculatedinsertion loss and crosstalk, respectively, of the switch 800 across thetelecom C-band. Here AMO and CRY stand for amorphous and crystallinestates, respectively.

During operation, when the GSST in the modulation layer 820 isamorphous, the phase matching condition between the two waveguides 810 aand 810 b is met. Accordingly, light launched into the first waveguide810 a (e.g., via the end 815 shown in FIG. 8B) is therefore evanescentlycoupled and efficiently transferred into the second waveguide 810 b, asdemonstrated by the intensity profile in FIG. 8C. Despite the largeoptical field overlap with the modulation layer 820 in this state, thelow material attenuation in amorphous GSST facilitates low-lossoperation. On the other hand, when the GSST in the modulation layer 820is in the crystalline state, input light almost exclusively couples intothe mode shown in FIG. 7D (i.e., an odd supermode) and remains in thefirst waveguide 810 a. FIG. 8D shows the intensity profile in this case.The minimal optical field interaction with the lossy crystalline GSSTlayer ensures low insertion loss. The simulated IL and crosstalk (i.e.,contrast ratio between the on/off states at the output ports) areplotted in FIGS. 8E and 8F, respectively. At 1550 nm, the 40-μm-longdevice attains an IL of about 0.4 dB and a CT of over 50 dB for thecrystalline state, and an IL as low as 0.06 dB and a CT of −27 dB in theamorphous state.

FIGS. 9A and 9B show a cross sectional view and a perspective view,respectively, of a 2×2 optical switch 900 using GSST alloy for lightrouting. The switch 900 includes three waveguides 910 a, 910 b, and 910c. A modulation layer 920 including the GSST alloy described herein isdisposed on the second waveguide 910 b. An optional cladding 930 can beused to surround the waveguides 910 a to 910 c. Light beams launchedinto the switch 900 via either the first waveguide 910 a or the thirdwaveguide 910 c can be routed out of the switch 900 via either the firstwaveguide 910 a or the third waveguide 910 c, depending on the state ofthe GSST in the modulation layer 920 (illustrated in FIGS. 9C and 9D).

An example set of dimensions of the switch 900 can be as follows. Thewidth w_(c) of the second waveguide 910 b can be about 512 nm. Thewidths w_(s) of the first waveguide 910 a and the third waveguide 910 ccan be about 730 nm. The width of the modulation layer w_(p) can beabout 400 nm. The spacing between adjacent waveguides w_(g) can be about562 nm. The heights of the three waveguides 910 a to 910 c can be about450 nm and the height of the modulation layer 920 can be about 60 nm.

FIGS. 9C and 9D show simulated optical fields in the 2×2 switch 900shown in FIGS. 9A and 9B when the GSST in the modulation layer 920 is inthe amorphous state and the crystalline state, respectively. Thesimulation uses the dimensions as described above. FIGS. 9E and 9F arecalculated insertion loss and crosstalk, respectively, of the 2×2 switchshown in FIGS. 9A and 9B across the telecom C-band.

The working principle of the switch 900 can be illustrated using thesupermode theory, where the three supermodes of the three waveguides 910a to 910 c are approximated as linear combinations of the normalizedindividual waveguide modes (labeled as |1>, |2>, and |3> for the firstwaveguide 910 a, the second waveguide 910 b, and the third waveguide 910c, respectively):

$\begin{matrix}{{{\frac{1}{2}{1\rangle}} + {\frac{\sqrt{2}}{2}{2\rangle}} + {\frac{1}{2}{3\rangle}}},\mspace{14mu} {{\frac{\sqrt{2}}{2}{1\rangle}} - {\frac{\sqrt{2}}{2}{3\rangle}}},{{and}\mspace{14mu}  - {\frac{\sqrt{2}}{2}{2\rangle}} + {\frac{1}{2}{3\rangle}}}} & (1)\end{matrix}$

It can be shown that complete power transfer (i.e., zero crosstalk) inthe cross state (FIG. 9C) can occur when the propagation constants(i.e., wave vectors) of the three supermodes are evenly spaced. In thiscase, a light beam launched into the switch 900 via the first waveguide910 a is first coupled into the second waveguide 910 b and then to thethird waveguide 910 c, where the light beam is coupled out of the switch900. In FIG. 9D, when the GSST is in the crystalline state, a light beamlaunched into the switch 900 via the first waveguide 910 a continues topropagate within the first waveguide 910 a.

The switch 900 also exhibits broadband switching capability across theC-hand as illustrated in FIGS. 9E and 9F. At 1550 nm, the ILs for thecross and bar states are 0.013 and 0.32 dB, and the CTs for the twostates are −37 and −32 dB, respectively. These figures represent, to thebest of the inventors' knowledge, the best performance for nonvolatileon-chip optical switches.

To elucidate the respective contributions to this exceptionalperformance from: (1) substitution of GST with GSST; and (2) thenon-perturbative configurations of the switches 800 and 900, simulationswere performed based on a GST alloy as well as a traditional MZI design.In the MZIs, one of the interferometer arms is loaded with a thin layerof PCM to induce a π phase shift upon crystallization. The powersplitting ratios in the arms are chosen to balance the MZI arms when thePCM is in the amorphous state, which can maximize the CT. However, whenthe PCM is crystallized, its increased absorption results in powerimbalance between the arms, compromising both the CT and IL. It can beshown that performance of MZI switches is defined by the classical FOM.Results in Table 1, which indicate that the combination of the GSSTmaterial and the non-perturbative configuration reaches the performancetarget, highlight the contribution from both material properties and thedevice configuration.

TABLE 1 Performance Comparison between Different 2 × 2 Switch DesignsTraditional MZI Nonperturbative Design GST GSST GST GSST IL (dB) 8.6 3.52.5 0.32 CT (dB) −0.02 −6.1 −20 −32

FIG. 10A shows a schematic of an 8×8 Benes network 1000 based onnonvolatile switches (e.g., switches 900 shown in FIGS. 9A and 9B). Thenetwork 1000 includes 8 input waveguides 1010 to deliver input lightbeams into a network of interconnected 2×2 switches 1020 and 8 outputwaveguides to deliver the output beams. FIG. 10B shows a schematic ofthe network 1000 extended to a dimension of 2^(m)×2^(m), illustratingthe recurrence relation between a 2^(m)×2^(m) switch and 2^(m−1)×2^(m−1)switch. In this case, the network of switches 1020 includes a firstgroup of 2^(m−1)×2^(m−1) switches 1022 to receive half of the inputlight beams and a second group of 2^(m−1)×2^(m−1) switches 1024 toreceive the other half of the input light beams. The level-m switchshown in FIG. 10B includes two level-(m−1) switches i.e., 1022 and 1024and 2^(m)2×2 switches. FIG. 10C shows calculated insertion losses of theswitch at 1550 nm. The all-cross state corresponds to I2^(m−1)-O^(2m−1)(the route along I8-1025a-1025b-1025c-1025d-O3 marked in FIG. 10A forthe 8×8 case). The all-bar state is the I^(2m−1)-O^(2m−1) path (theroute along I4-1026a-1026b-1026c-1025d-O4 marked in FIG. 10A).

The network 1000 uses the 2×2 switch as a building block and can bescaled to realize arbitrary network complexity levels. As an example,FIG. 10A depicts the block diagram for an 8×8 switch, and FIG. 10Billustrates the generic scaling law to construct a 2^(m)×2^(m) switch.Generally, a 2^(m)×2^(m) switch includes of 2^(m−1) rows and 2^(m−1)columns of 2×2 switches. Therefore, light passes through a total of2^(m−1)2×2 switches in the fabric.

The IL of the entire network can be computed by considering ILs fromindividual 2×2 switches on the optical path as well as loss due towaveguide crossings. The IL of a waveguide crossing is taken as 0.1 dB,which has been experimentally realized in the C-band. Because the 2×2switch element has higher IL in the bar state (see, e.g., FIG. 9E), theILs of all-bar and all-cross states approximately correspond to theupper and lower bounds of the network IL. As used herein, all-bar statemeans all of the 2×2 switch states in a light path bar-state andall-cross state means all of the 2×2 switch states in a light path arecross-state. For the all-bar state, I^(2m−1)-O^(2m−1) represents a lossypath with a large number of crossings. The IL for this path is:

(2^(m)−2)×0.1 dB+2m−1×0.32 dB   (2)

An exemplary all-cross state path is I^(2m)-O^(2m−1) and thecorresponding IL is:

(3×2^(m−1)−1−2m)×0.1 dB+(2m−1)×0.013 dB   (3)

This IL is dominated by the waveguide crossing loss. The CT, defined asthe ratio of transmitted power from the target output port over themaximum leaked power from a “nontarget” port, is estimated using thefollowing formula at 1550 nm for a 2^(m)×2^(m) switch:

−(32 dB−10·log₁₀ m dB)   (4)

where −32 dB is the “worst-case” (bar state) CT for a 2×2 switch, andthe second factor adds up leaked power from each switch stage.

FIG. 10C shows the all-bar and all-cross its versus the network level infollowing Equations (2) and (3). In a 16×16 switch, the ILs forall-cross and all-bar states are 1.6 and 3.6 dB, respectively, and theILs in a 32×32 switch are 3.9 and 5.9 dB. The CTs for a 16×16 switch anda 32×32 switch are −26 and −25 dB, respectively. These figures representa significant improvement compared to state-of-the-art (volatile)on-chip switches. For example, for 16×16 switches, the reported ILs are6.7 and 14 dB, and the CT is −15.1 dB. The corresponding ILs are 12.9and 16.5 dB in 32×32 switches, and the CT is approximately −15 dB.

FIG. 11A shows a schematic of a modulator 1100 including a ringresonator 1110 and a modulation layer 1120 made of the GSST alloydescribed herein. The modulator 1100 also includes a waveguide 1130evanescently coupled to the ring resonator 1110, which is employed tocouple optical input 1105 a into the ring resonator 1110 and coupleoptical output 1105 b out of the ring resonator 1110. FIG. 11B is amicroscope image of two modulators similar to the modulator shown inFIG. 11A. the modulator 1100 shown in FIG. 11A. FIG. 11C shows thetransmission spectra of the modulator when the GSST material is in itscrystalline state and amorphous state.

During operation, the optical mode in the waveguide 1130 and the ringresonator 1110 is coupled into the modulation layer 1120. Therefore, thechange in the refractive index and extinction ratio of the modulationlayer 1120 can affect the relative mode property. As illustrated in FIG.11C, when the GSST (e.g., Ge₂Sb₂Se₄Te₁) is in the amorphous state, themodulator is turned ON, i.e., the optical mode is in resonance with thering resonator 1110 so the transmission of light at the resonantwavelength (about 1558.2 nm) is low. When the GSST is crystallized(i.e., the modulator is turned OFF), the optical loss in the materialdominates the round trip loss in the ring resonator, the dip in thetransmission spectrum disappears and the modulator 1100 behaves like awaveguide that passes the light beam. FIG. 11C also shows that the ratioof the output power at the resonant wavelength when the modulator is ONand OFF can be substantially equal to or greater than −40 dB.

FIG. 12 shows a schematic of an interferometer 1200 using GSST alloy forphase modulation. The interferometer 1200 includes an input waveguide1210 to receive optical input 1202, which is then split into two anus1220 a and 1220 b. A modulation layer 1230 made of the GSST alloydescribed herein is disposed on the first arm 1220 a to introduce aphase shift in the light propagating in the first arm 1220 a. Theinterferometer 1200 also includes an output waveguide 1240 to deliverthe optical output 1204, which is generated via interference of thelight beams delivered by the two arms 1220 a and 1220 b. Switching theGSST in the modulation layer 1230 can introduce a phase shift betweenthe light beams, thereby changing the interference at the outputwaveguide 1240. For example, when the GSST is in the amorphous state,the two light beams out of the two arms 1220 a and 1220 b canconstructively interfere with each other. When the GSST is in thecrystalline state, the two light beams out of the two arms 1220 a and1220 b can destructively interfere with each other.

FIG. 13 shows a schematic of a pixel array 1300 integrated with a GSSTalloy for spatial light modulation. In this array 1300, each pixel 1310can be coated with a layer of GSST, which can be used to tune thereflectance, transmittance, or spectral response of the pixel 1310. Thereflectance/transmittance or spectral response of the pixel depends onthe absorption or resonance behavior of the GSST layer. Therefore, bychanging the state of GSST, the absorption or the resonance behaviorwill be changed, thus the reflectance/transmittance or spectral responseof the pixel can be tunable.

Methods of Manufacturing GSST Alloy and Depositing GSST Films

FIGS. 14A-14D illustrate a method 1400 of manufacturing GSST alloysdescribed herein. In this method 1400, an initial composition 1430 isplaced into a container 1420 (e.g., a tube), which is put in a glove box1410, as illustrated in FIG. 14A. The initial composition 1430 includesthe elements Ge, Sb, Se, and Te with the proper atomic percentages ofeach element (e.g., the compositions described with reference to FIG.1A). In one example, the initial composition 1430 can include a GSTalloy and Se to replace some of the Te by Se. In another example, theinitial composition 1430 can include GST and GeSbSe.

FIG. 14B shows that vacuum condition is created in the container 1420containing the initial composition 1430 to drive out water vapor,followed by sealing of the container 1420 (e.g., using a torch). In FIG.14C, the container 1420 is placed into a furnace 1450 (e.g., a rockingfurnace) to melt the composition in the container. Is this process, theinitial composition 1430 is melted down so as to form a GSST alloy. Theswinging of the furnace 1450 can increase the composition uniformityafter melting. The resulting alloy is then quenched down to roomtemperature, as shown in FIG. 14D. The manufactured GSST alloy is inbulk form and can be ground into powder that can be used as thedeposition source for thermal evaporation (see FIG. 15 below).

FIG. 15 shows a schematic of a system 1500 to fabricate a GSST film viathermal deposition. The system 1500 includes a vacuum chamber 1510. Asource 1520 including GSST (e.g., GSST powder manufactured via themethod 1400 illustrated in FIGS. 14A-14D) is placed in the vacuumchamber 1510 and in thermal communication with a heat source 1530. Theheat source 1530 heats up the source 1520, causing the GSST material toevaporate and form a GSST flow 1525. A target substrate 1540 is placedabove the source 1520 and in the path of the GSST flow 1525. Atoms ofGSST in the GSST flow 1525 are deposited on the target substrate 1540 toform a GSST thin film. The distance between the source 1520 and thetarget substrate 1540 can be, for example, about 200 mm to about 1meter. Due to the vacuum condition and the relatively low temperatureused in thermal evaporation, the resulting GSST film is usually in theamorphous state and can be switched to the crystalline state by anannealing process described above (e.g., with reference to FIG. 6).

FIG. 16 shows a system 1600 to fabricate GSST thin films via sputtering.The system 1600 includes a chamber 1610 holding a sputtering target1620, which can be a single GSST target or multiple targets, such as Ge,Sb, Se and Te, or GeSbTe and GeSbSe. The chamber 1610 includes an inputport 1615 a to receive sputtering gas (e.g., Argon) to create ions(e.g., Ar⁺ ions) that can eject out atoms in the sputtering target 1620via bombardment. The ejected atoms then land on a substrate 1630disposed above the sputtering target 1620 to form a GSST thin film.

Conclusion

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e., “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

1. An alloy of Ge_(x)Sb_(y)Sb_(z)Se_(z)Te_(m), wherein atoms of Ge, Sb,Se, and Te form a crystalline structure having a plurality of vacanciesrandomly distributed in the crystalline structure.
 2. The alloy of claim1, wherein x+y is about 0.4 to about 0.5, z is about 0.1 to 0.54, andx+y+z+m=1.
 3. The alloy of claim 1, wherein x is about 0 to 0.15, y isabout 0.5 to about 0.68, z is about 0.05 to 0.3, and x+y+z+m=1.
 4. Thealloy of claim 1, wherein the plurality of vacancies has an atomicpercentage of about 0.5% to about 20% in the alloy.
 5. The alloy ofclaim 1, wherein a transition temperature of the alloy is about 150degrees Celsius to about 400 degrees Celsius.
 6. The alloy of claim 1,wherein a resistivity of the alloy is substantially equal to or greaterthan 1 Ω·cm.
 7. The alloy of claim 1, wherein the alloy has a firstrefractive index n₁ in an amorphous state and a second refractive indexn₂, greater than the first refractive index by at least 1, in acrystalline state.
 8. The alloy of claim 7, wherein the alloy has anextinction coefficient k substantially equal to or less than 10⁻³ in thecrystalline state.
 9. The alloy of claim 7, wherein a figure of merit(FOM) of the alloy is substantially equal to or greater than 5, whereFOM=(n₂−n₁)/k, and k is an extinction coefficient of the alloy in thecrystalline state,
 10. An optical device, comprising: a first opticalelement; and a second optical element comprising the alloy of claim 1and disposed in optical communication with the first optical element,wherein the first optical element is configured to provide opticalconfinement of a light beam and the second optical element is configuredto modulate electromagnetic field distribution within the first opticalelement.
 11. A modulator, comprising: a waveguide; and a modulationlayer comprising the alloy of claim 1 disposed on the waveguide, themodulation layer being switchable between an amorphous state and acrystalline state.
 12. The modulator of claim 11, wherein the waveguideis a first waveguide and forms at least a portion of a ring resonator,and the modulator further comprises: a second waveguide, evanescentlycoupled to the ring resonator, the second waveguide comprising an inputsection to couple an input light beam into the ring resonator and anoutput section to propagate an output light beam out of the ringresonator.
 13. The modulator of claim 12, wherein the ring resonator isconfigured to deliver a first output beam having a first power when themodulation layer is in the amorphous state and deliver a second outputbeam having a second power when the modulation is in the crystallinestate, and a ratio of the second power of the second output beam to thefirst power of the first output beam is substantially equal to orgreater than 40 dB.
 14. An interferometer, comprising: a first waveguideto guide a first beam; a second waveguide, in evanescent communicationwith the first waveguide, to guide a second beam; and a modulation layercomprising the alloy of claim 1, disposed on the first waveguide, tochange a coupling ratio between the first waveguide and the secondwaveguide.
 15. A method of modulating a light beam propagating in awaveguide, the method comprising: heating a modulation layer, in opticalcommunication with the waveguide, to a first temperature, the modulationlayer comprising an alloy of Ge_(x)Sb_(y)Se_(z)Te_(m) switchable betweenan amorphous state and a crystalline state, wherein the firsttemperature is greater than a phase transition temperature of the alloyand less than about 100 degrees Celsius above the phase transitiontemperature, and the heating causes the alloy to form a crystallinestructure having a plurality of vacancies randomly distributed in thecrystalline structure.
 16. The method of claim 15, wherein heating themodulation layer comprises heating the modulation using a heater inthermal communication with the modulation layer.
 17. The method of claim15, wherein heating the modulation layer comprises illuminating themodulation layer with a laser pulse.
 18. The method of claim 15, whereinthe first temperature is about 200 degrees Celsius to about 300 degreesCelsius.
 19. The method of claim 15, wherein the modulation layercomprises a film of the alloy deposited on the waveguide and having hasa thickness substantially equal to or less than 1 μm.
 20. The method ofclaim 15, further comprising: heating the modulation layer to a secondtemperature greater than the first temperature; and cooling themodulation layer at a cooling rate substantially equal to or greaterthan about 10⁵ degrees Celsius per second so as to change the alloy fromthe crystalline state to the amorphous state.
 21. The method of claim20, wherein the cooling of the modulation layer causes the modulationlayer to guide about 1% to about 50% of the light beam in the modulationlayer.
 22. An apparatus, comprising: a first waveguide to guide a lightbeam; and a modulation layer disposed on the first waveguide, themodulation comprising an alloy of Ge_(x)Sb_(y)Se_(z)Te_(m) having afirst refractive index n₁ in an amorphous state and a second refractiveindex n₂, greater than the first refractive index by at least 1, in acrystalline state, wherein the first waveguide and the modulation layerare configured to guide about 1% to about 50% of the light beam in themodulation layer when the alloy is in the amorphous state.
 23. Theapparatus of claim 22, wherein the first waveguide has a thirdrefractive index substantially equal to the first refractive index ofthe alloy when the alloy is in the amorphous state.
 24. The apparatus ofclaim 22, wherein the alloy has a plurality of randomly distributedvacancies in the crystalline state.
 25. The apparatus of claim 22,wherein a resistivity of the alloy is substantially equal to or greaterthan 1 Ω/cm.
 26. The apparatus of claim 22, wherein the alloy has anextinction coefficient k substantially equal to or less than 10⁻³ in thecrystalline state.
 27. The apparatus of claim 22, wherein a figure ofmerit (FOM) of the alloy is substantially equal to or greater than 5,where the FOM=(n₂−n₁)/k, and k is an extinction coefficient of thealloy.
 28. The apparatus of claim 22, further comprising: a secondwaveguide evanescently coupled to the first waveguide, wherein themodulation layer is configured to divert the light beam into the secondwaveguide when the alloy is in the crystalline state.
 29. The apparatusof claim 22, further comprising: a second waveguide evanescently coupledto the first waveguide and disposed on a first side of the firstwaveguide; and a third waveguide evanescently coupled to the firstwaveguide and disposed on a second side, opposite the first side, of thefirst waveguide, wherein the modulation layer is configured to divertthe light beam into the second waveguide when the alloy is in theamorphous state and divert the light beam into the third waveguide whenthe alloy is in the crystalline state.